If the purpose of the nervous system is information processing, then we should be able to say what it means for a biological system to process information. Unfortunately, little can be said in a quantitative way. To address this question attempts have intermittently been made over the last 50 years to understand brain function by applying information theory (IT). In recent years, such attempts have become more frequent, with occasional, interesting successes. However, from the viewpoint of the engineering discipline of IT, these attempts have hardly scratched the surface of what IT has to offer, and so far, people have only attempted to incorporate the most well-known and elementary aspects of IT. Indeed, the ideas applied with apparent success - source coding theory - are essentially as old as Shannon's original work. Since that time much has occurred in IT, including several extensions of Shannon's work. Here the investigators advocate the introduction of RD theory and its recent offspring, successive refinement theory. It is the goal of the proposed research to create a demonstration illustrating the applicability and promising superiority of these more sophisticated results of IT. The investigators will translate the ideas of rate-distortion theory and successive refinement theory from the communication literature, where they were developed, to the issues of biological computation. This translation will necessarily be abstract and mathematical. At the same time, however, the investigators will further show people how to apply these insights as well as test several conjectures. Biologically motivated computer simulations of small examples, examples well within the purview of neural network theory and the issues inherent in studying the computational basis of cognition, will be used to illustrate the theory being developed. Finally, the investigators describe how RD theory and the dynamics inherent in the translated version of successive refinement theory can be used to quantify some of the most pervasive metaphors of neural computation. Thus although there is tremendous promise in using the known results of IT, the investigators believe that neuroscientists must begin by applying some of the deeper aspects of the theory. In particular, the overly simplistic uses of IT which now exist in the neuroscientific literature must be clarified and upgraded. The proposed approach is innovative because it has not been done before in the way proposed and it is important to the mission of NIH because understanding the brain is important to the mission of NIH. Many diseases and disabilities result from impaired or damaged brain function. The list is long: drug abuse, blindness, memory and cognitive impairments due to aging, deafness, learning disabilities in children, all types mental illness, post-traumatic stress disorder, epilepsy, traumatic brain injury, stroke, etc. If the goal is to repair, prevent, and treat such maladies, a fundamental, deep understanding of what neuronal activity signifies and what this activity means in terms of thought processes, sensations, motivations, and our ability to affect the world will benefit from an improved theory neural information processing.